Three-dimensional manifolds having metrics with the same geodesics

被引：17

作者：

Matveev, VS ^{[1
]}

机构：

[1] Univ Freiburg, Math Inst, D-79104 Freiburg, Germany

来源：

TOPOLOGY | 2003年 / 42卷 / 06期

关键词：

geodesic equivalence; projectively equivalent metrics; projective connection; integrable system; separation of variables; geodesic rigidity; Liouville metric; Stackel system; obstructions to integrability; local product structure; lens space;

D O I：

10.1016/S0040-9383(03)00004-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if two Riemannian metrics have the same geodesics on a closed three-dimensional manifold which is homeomorphic neither to a lens space nor to a Seifert manifold with zero Euler number, then the metrics are proportional. (C) 2003 Elsevier Science Ltd. All rights reserved.

引用

页码：1371 / 1395

页数：25

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